Circle Theorems: WJEC GCSE Higher November 2023 Unit 1 Q10

Higher November 2023 Unit 1 Q10

WJECHigherCurrent spec3 marksCircle Theorems

10. The points \(B\), \(C\), \(D\) and \(E\) lie on the circumference of a circle, with centre \(O\).
\(AF\) is a tangent to the circle.
\(AO\) is a straight line.

Circle centre O with B, C, D, E on the circumference; tangent AF touches at B; line A–E–O; angle BAO = 42°; chords BD, BC, EC, ED and radius OB; angle x at D between DE and DB

Diagram not drawn to scale

Calculate the size of angle \(x\).
You must show all your working. [3]

Mark scheme

Scheme	Marks	Comments
(\(AOB\) =) 180 – 90 – 42 or 90 – 42	M1	Check diagram for answers. Note: 180 – 132
48(°)	A1	May be implied by sight of a final answer of 24.
\(x\) = 24(°)	B1	FT ‘their 48’ ÷ 2, provided ‘their 48’ ≠ 42.

10. Alternative method

Scheme	Marks	Comments
(\(x\) = ) \(\dfrac{180 - 90 - 42}{2}\) or \(\dfrac{90 - 42}{2}\)	M2	Check diagram for answers. Award M2 for complete method.
\(x\) = 24(°)	A1